2/3sqrt{20}*(1/3sqrt{48})divsqrt{22/3} eching

$$\frac { 2 } { 3 } \sqrt { 20 } \times ( \frac { 1 } { 3 } \sqrt { 48 } ) \div \sqrt { 2 \frac { 2 } { 3 } }$$

Baholash

$$\frac{4\sqrt{10}}{3}\approx 4,216370214$$

Yechim qadamlari

Faktor: 20=2^{2}\times 5. \sqrt{2^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{2}{3}\times 2\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

\frac{2}{3}\times 2 ni yagona kasrga aylantiring.

$$\frac{\frac{2\times 2}{3}\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

4 hosil qilish uchun 2 va 2 ni ko'paytirish.

$$\frac{\frac{4}{3}\sqrt{5}\times \frac{1}{3}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Suratni maxrajga va maxrajini suratga ko‘paytirish orqali \frac{4}{3} ni \frac{1}{3} ga ko‘paytiring.

$$\frac{\frac{4\times 1}{3\times 3}\sqrt{5}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

\frac{4\times 1}{3\times 3} kasridagi ko‘paytirishlarni bajaring.

$$\frac{\frac{4}{9}\sqrt{5}\sqrt{48}}{\sqrt{\frac{2\times 3+2}{3}}}$$

Faktor: 48=4^{2}\times 3. \sqrt{4^{2}\times 3} koʻpaytmasining kvadrat ildizini \sqrt{4^{2}}\sqrt{3} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 4^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{4}{9}\sqrt{5}\times 4\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

\frac{4}{9}\times 4 ni yagona kasrga aylantiring.

$$\frac{\frac{4\times 4}{9}\sqrt{5}\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

16 hosil qilish uchun 4 va 4 ni ko'paytirish.

$$\frac{\frac{16}{9}\sqrt{5}\sqrt{3}}{\sqrt{\frac{2\times 3+2}{3}}}$$

\sqrt{5} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{2\times 3+2}{3}}}$$

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{6+2}{3}}}$$

8 olish uchun 6 va 2'ni qo'shing.

$$\frac{\frac{16}{9}\sqrt{15}}{\sqrt{\frac{8}{3}}}$$

\sqrt{\frac{8}{3}} boʻlinmasining kvadrat ildizini \frac{\sqrt{8}}{\sqrt{3}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{\sqrt{8}}{\sqrt{3}}}$$

Faktor: 8=2^{2}\times 2. \sqrt{2^{2}\times 2} koʻpaytmasining kvadrat ildizini \sqrt{2^{2}}\sqrt{2} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 2^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}}{\sqrt{3}}}$$

\frac{2\sqrt{2}}{\sqrt{3}} maxrajini \sqrt{3} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}$$

\sqrt{3} kvadrati – 3.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{2}\sqrt{3}}{3}}$$

\sqrt{2} va \sqrt{3} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\frac{16}{9}\sqrt{15}}{\frac{2\sqrt{6}}{3}}$$

\frac{16}{9}\sqrt{15} ni \frac{2\sqrt{6}}{3} ga bo'lish \frac{16}{9}\sqrt{15} ga k'paytirish \frac{2\sqrt{6}}{3} ga qaytarish.

$$\frac{\frac{16}{9}\sqrt{15}\times 3}{2\sqrt{6}}$$

\frac{\frac{16}{9}\sqrt{15}\times 3}{2\sqrt{6}} maxrajini \sqrt{6} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{16}{9}\sqrt{15}\times 3\sqrt{6}}{2\left(\sqrt{6}\right)^{2}}$$

\sqrt{6} kvadrati – 6.

$$\frac{\frac{16}{9}\sqrt{15}\times 3\sqrt{6}}{2\times 6}$$

\frac{16}{9}\times 3 ni yagona kasrga aylantiring.

$$\frac{\frac{16\times 3}{9}\sqrt{15}\sqrt{6}}{2\times 6}$$

48 hosil qilish uchun 16 va 3 ni ko'paytirish.

$$\frac{\frac{48}{9}\sqrt{15}\sqrt{6}}{2\times 6}$$

\frac{48}{9} ulushini 3 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\frac{16}{3}\sqrt{15}\sqrt{6}}{2\times 6}$$

\sqrt{15} va \sqrt{6} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\frac{16}{3}\sqrt{90}}{2\times 6}$$

12 hosil qilish uchun 2 va 6 ni ko'paytirish.

$$\frac{\frac{16}{3}\sqrt{90}}{12}$$

Faktor: 90=3^{2}\times 10. \sqrt{3^{2}\times 10} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{10} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{16}{3}\times 3\sqrt{10}}{12}$$

3 va 3 ni qisqartiring.

$$\frac{16\sqrt{10}}{12}$$

\frac{4}{3}\sqrt{10} ni olish uchun 16\sqrt{10} ni 12 ga bo‘ling.

$$\frac{4}{3}\sqrt{10}$$